桥联重积分方程一种新的数值方法

GOVERNING FIBER - BRIDGED

纤维增强复合材料断裂力学中的桥联问题常常可归结为一个二重积分方程。常见的求解方法有矩阵迭代法和积分迭代法,但这两种方法都较复杂。本文给出一种新的分段插值方法,对此积分方程进行求解。数值计算结果表明,该方法效果令人满意。

The fiber - bridged problem of fiber reinforced composites fracture mechanics may often results in a double integral equation. To solve it, the matrix iterative method and the integral iterative method are used in [1,2]. But these two methods are not simple. We present an interpolation method for solving the fiber -bridged integral equation. As described in section 1, we first divide the integration interval into many pieces, then for such piece we give an interpolation function (equation (3)) to approach the integral function. In this way, the solution of the integral equation is changed into an algebra problem. Calculation results as given in Figures 1, 2 and 3 show preliminarily that our method is effective and reliable.